We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and those by some advanced combinatorial algorithms in [Ann. Oper. Res. 248 (2017) 365] are at least $0.986$ and can be further improved to at least $0.997$ by a preliminary attempt to break out of local optima.

翻译：我们通过充分利用一个等价的连续形式，提出了一种用于最大割问题的简单迭代(SI)算法。该算法完全无需舍入操作，并具有以下优势：所有子问题均具有显式解析解，割值单调递增，且通过适当的次梯度选择，迭代点可在有限步内收敛至局部最优解。在G-set数据集上的数值实验验证了其性能。特别地，SI算法取得的最佳割值与文献[Ann. Oper. Res. 248 (2017) 365]中某些先进组合算法的比值至少达到0.986，通过初步尝试跳出局部最优解，该比值可进一步提升至至少0.997。